https://re-st.github.io/blog/%EC%B5%9C%EC%A0%81%ED%99%94/ Recent content in 최적화 on Park, Geon (re-st) Hugo ko-kr Copyright © 2026, Geon Park. Fri, 01 May 2026 18:45:35 +0900 https://re-st.github.io/seminar/%EC%A0%84%EC%82%B0-%EC%84%B8%EB%AF%B8%EB%82%98-%EA%B7%BC%EC%82%AC-%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98%EA%B3%BC-%EC%B5%9C%EC%A0%81%ED%99%94-%EB%AC%B8%EC%A0%9C-2018-%EA%B0%80%EC%9D%84-kaist/ Sat, 01 Sep 2018 00:00:00 +0900 https://re-st.github.io/seminar/%EC%A0%84%EC%82%B0-%EC%84%B8%EB%AF%B8%EB%82%98-%EA%B7%BC%EC%82%AC-%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98%EA%B3%BC-%EC%B5%9C%EC%A0%81%ED%99%94-%EB%AC%B8%EC%A0%9C-2018-%EA%B0%80%EC%9D%84-kaist/ <blockquote> <p>KAIST 전산 세미나, 2018 가을학기. 16pm. 발표자 미상.</p> </blockquote> <h1 id="approximation-algorithm-for-optimization-problem">Approximation Algorithm for Optimization Problem</h1> <h2 id="mathematical-optimization">Mathematical Optimization</h2> <ul> <li><strong>Input</strong>: feasible solutions 집합, objective function \(f\)</li> <li><strong>Output</strong>: \(f(x)\)를 최대화/최소화하는 \(x\)</li> <li><strong>Running time</strong>: \(\text{poly}(|l|)\) — \(l\)을 표현하는 비트 수</li> </ul> <h2 id="least-square-regression">Least Square Regression</h2> <ul> <li>Input: \(A \in \mathbb{R}^{m \times n}\), \(b \in \mathbb{R}^m\)</li> <li>Feasible set: \(x \in \mathbb{R}^n\)</li> <li>\(f(x) = \|Ax - b\|^2\)</li> </ul> <h2 id="discrete-optimization-vertex-cover">Discrete Optimization (Vertex Cover)</h2> <ul> <li>Input: \(G = (V, E)\)</li> <li>Feasible set: \(C \subseteq V\), \(C\)가 모든 edge를 cover</li> <li>\(f(C) = |C|\), 최소화 → <strong>NP-hard</strong> [Karp 72]</li> </ul> <h2 id="핵심-관찰">핵심 관찰</h2> <blockquote> <p>&ldquo;Almost every combinatory algorithm is either NP-complete or Polynomial solvable.&rdquo; — Williams 2013</p>